gravity assist

Also known as the slingshot effect, an important spaceflight
technique used successfully on a number of interplanetary missions, including
Voyager, Galileo,
and Cassini, whereby the gravitational
field of a planet is used to increase the speed and alter the course
of a spacecraft without the need to expend fuel. The inbound flight path
is carefully chosen so that the spacecraft will be whipped around the assisting
body, being both accelerated and deflected on a hyperbolic trajectory. At
first sight, it may seem as if something has been gained for nothing. However,
the additional speed of the spacecraft has been won at the planet's expense
which, as a result of the encounter, slows imperceptibly in its orbit and,
as a result, moves fractionally closer to the Sun.

One of the earliest, and most dramatic applications of the technique came
in 1970 when the world watched as NASA used a lunar gravity-assist to rescue
the Apollo 13 astronauts after an
onboard explosion had severely damaged their spacecraft en route to the
Moon. By using a relatively small amount of fuel to put the spacecraft onto
a suitable trajectory, NASA engineers and the astronauts were able to use
the Moon's gravity to turn the ship around and send it back home.

Gravity assist primer

The following description of a gravity assist maneuver comes from the Jet
Propulsion Laboratory and applies to the Voyager spacecraft's encounter
with Jupiter.

From Jupiter's point of view, the situation is similar to a
bicyclist speeding up going downhill into a valley, then slowing down
again on the uphill part of the road.

In the vector diagram at left, the situation
is simplified to two dimensions. You can see the magnitude and direction
of the spacecraft's velocity on its way in towards Jupiter in the lower
right. At the upper left, you can see that the accelerating force of Jupiter's
gravitation has made a significant change in the direction of the spacecraft's
velocity, but not in its magnitude. (These represent velocity at "infinity,"
from Jupiter, that is, before and after being noticeably changed by Jupiter's
presence.) Near the middle of the diagram, the long arrow shows that there's
a significant, but temporary, increase in the magnitude (speed). Note
these speeds are all with respect to Jupiter.

To look at the same phenomenon in terms of a cyclist, VIN shows
the cyclist approaching a downhill grade into a canyon. VOUT
shows that the cyclist slowed down again at the top of the ensuing uphill
grade (of course this cycling analogy asks us to ignore air friction and
vehicle friction, etc., which are virtually absent in the spacecraft's
case). Indeed, after negotiating the canyon, the cyclist's direction has
changed, but in the end s/he has not made a lasting change in speed (unless
you don't ignore all that friction etc.).

The planet's own motion is a key. A gravity assist with Jupiter involves
not a stationary planet as considered above, but a planet with enormous
angular momentum as it revolves around the Sun. In the diagram at right,
Jupiter's motion along its solar orbit has been illustrated with a vector
colored red (simplified, of course: Jupiter revolves along an arc, not
a straight line. Imagine the Sun situated below the bottom of the diagram).
The spacecraft acquires this Sun-relative vector, or a significant portion
of it, during its interaction with Jupiter.

You can see how the red vector is added to VIN and VOUT.
The resulting vector shows how the spacecraft's velocity, relative to
the Sun, takes on a nice boost from Jupiter. Notice how rotation of the
vector from VIN to VOUT (the bending of the spacecraft's
path by the planet's gravity) helps increase the result. This trajectory
bending is the other key.

The spacecraft is a physical mass, so it has its own gravitation. That's
how the spacecraft can tug on Jupiter and actually decrease the planet's
orbital momentum by a tiny amount. In the exchange, the spacecraft acquires
momentum from Jupiter – a significant amount, compared to the momentum
the spacecraft already had.

History of gravity assist in science and science fiction

Historians of science differ on the issue of when gravity assist as a technique
in spaceflight was first discussed in the scientific literature. The mathematics
of how cometary orbits are affected by close approaches to planets was known
in the late 18th century and in the early 1920s, Walter Hohmann
showed that the lowest energy path between any two planets is an ellipse
that is tangential to the orbits of both the planets. The first mention
of a gravity-assist maneuver may have been by Ray Cummings in his science
fiction story "Brigands of the Moon," first published in Astounding
in 1931. In this story, an Earth spaceship is piloted by martian brigands
who are determined to get their hands on the Moon's one key resource, radiactum
("the catalyst mineral which was revolutionising industry"):

We were at this time no more than some sixty-five
thousand miles from the moon's surface. The Planetara presently would
swing upon her direct course for Mars. There was nothing that would cause
passenger comment in this close passing of the moon; normally we used
the satellite's attraction to give us additional starting speed.

The concept of gravity assist as a means of altering the speed or course
of a spacecraft does not appear in scientific literature, however, for another
two decades. In a footnote Arthur C. Clarke
mentions a paper by Derek Lawden titled "Perturbation Manoeuvres" (Journal
of the British Interplanetary Society, vol 13, no 5, Sept 1954). Lawden,
a mathematician, worked in the early 1950s on the optimization of rocket
trajectories. Somewhat later, in 1961, a summer intern at JPL, Michael A.
Minovitch, showed that the gravitational field of a planet could provide
thrust to a spacecraft. He demonstrated that careful design of the trajectory
to a target planet could provide a gravity assist to move from that planet
to another.